Which of the following statements about the ‘Financial Leverage’ and ‘Borrowing to Invest’ sections of the lecture material are TRUE: As long as the expected return on assets is greater than the cost of debt (interest rates), adding financial leverage to an investment magnifies both expected return on equity and also total risk of that equity. An investor has a margin loan on an Exchange Traded Fund that tracks the ASX200 index. The value of the investment (asset) is $100,000 and they have a $50,000 margin loan. If the ASX200 were to suddenly fall in value by 30%, that investor would likely experience a margin call.

Question

BlackTom AI · Accepted Answer

To tackle this question, I’ll examine each statement in turn and explain the rationale behind its truth or falsehood.

Option A: "Neither of the statements are true (both are false)". The first claim says that if the expected return on assets exceeds the cost of debt, adding financial leverage magnifies both the expected return on equity (ROE) and the total risk of that equity. In classic levered equity analysis, when ROA > cost of debt, using debt does amplify ROE and typically increases the risk (volatility) of the equity value, because debt introduces fixed financing costs and positions equity at a higher leverage level. Therefore, this statement would be incorrect if we accept that leverage can enhance ROE and equity risk under positive spread. The second claim provides a concrete margin loan example and asserts a margin call would likely occur after a 30% drop. With a $100k asset and $50k loan, a 30% fall reduces the asset to $70k, giving equity of $20k. The margin ratio is 20k/70k ≈ 28.6%. Whether a margin call occurs depends on the maintenance margin requirement, but it is plausible that a margin call would be triggered. Since at least one of the two statements tends to be plausible, labeling both as false would be inconsistent. Therefore, Option A is not correct.

Option B: "Only statement 1 is true". If statement 1 were true and statement 2 false, we would be saying leverage always magnifies ROE and equity risk when ROA exceeds cost of debt, but that the margin-call scenario would not happen with a 30% drop. As discussed, when asset value drops to 70k and equity to 20k, the margin ratio is around 28.6%, which commonly can trigger a margin call depending on the maintenance margin policy. Hence, declaring statement 2 false is dubious in typical margin loan setups. Consequently, Option B is not strongly supported.

Option C: "Only statement 2 is true". This would imply statement 1 is false, i.e., leveraging when ROA > cost of debt does not magnify ROE and equity risk. That contradicts standard financial theory about positive leverage increasing ROE and the risk of equity when debt costs are lower than asset returns. Therefore, this option is inconsistent with the usual interpretation and is unlikely to be correct.

Option D: "Both statements are true (neither are false)". Recalling the first statement, if ROA exceeds the cost of debt, financial leverage typically magnifies both ROE and the total risk of the equity, aligning with conventional leverage effects. For the second statement, with a $100k asset and a $50k margin loan, a 30% drop to $70k leaves equity at $20k and a margin ratio around 28.6%. Depending on the maintenance margin requirement, this scenario is commonly associated with a margin call risk, making the statement plausible.

Taking all options into account, the most coherent interpretation is that both statements align with standard leveraged finance concepts and margin mechanics, making Option D the best overall fit.

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